TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.4.099
TI  - Finite-size corrections to the energy spectra of gapless one-dimensional systems in the presence of boundaries
PY  - 2024/10/02
UR  - https://scipost.org/SciPostPhys.17.4.099
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 4
SP  - 099
A1  - Liu, Yifan
AU  - Shimizu, Haruki
AU  - Ueda, Atsushi
AU  - Oshikawa, Masaki
AB  - We present the finite-size scaling theory of one-dimensional quantum critical systems in the presence of boundaries. While the finite-size spectrum in the conformal limit, namely of a conformal field theory with conformally invariant boundary conditions, is related to the dimensions of boundary operators by Cardy, the actual spectra of lattice models are affected by both bulk and boundary perturbations and contain non-universal boundary energies. We obtain a general expression of the finite-size energy levels in the presence of bulk and boundary perturbations. In particular, a generic boundary perturbation related to the energy-momentum tensor gives rise to a renormalization of the effective system size. We verify our field-theory formulation by comparing the results with the exact solution of the critical transverse-field Ising chain and with accurate numerical results on the critical three-state Potts chain obtained by Density-Matrix Renormalization Group.
ER  -

@Article{10.21468/SciPostPhys.17.4.099,
	title={{Finite-size corrections to the energy spectra of gapless one-dimensional systems in the presence of boundaries}},
	author={Yifan Liu and Haruki Shimizu and Atsushi Ueda and Masaki Oshikawa},
	journal={SciPost Phys.},
	volume={17},
	pages={099},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.4.099},
	url={https://scipost.org/10.21468/SciPostPhys.17.4.099},
}